Rational q× q Carathéodory Functions and Central Non-negative Hermitian Measures

Original · EN

We give an explicit representation of central measures corresponding to finite Toeplitz non-negative definite sequences of complex q× q matrices. Such measures are intimately connected to central q× q Carathéodory functions. This enables us to prove an explicit representation of the non-stochastic spectral measure of an arbitrary multivariate autoregressive stationary sequence in terms of the covariance sequence.